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Date	May 2017	Marks available	3	Reference code	17M.3.HL.TZ1.5
Level	Higher level	Paper	Paper 3	Time zone	1
Command term	Calculate	Question number	5	Adapted from	N/A

Question

A proton is accelerated from rest through a potential difference V to a speed of 0.86c.

Calculate the potential difference V.

[3]

The proton collides with an antiproton moving with the same speed in the opposite direction. As a result both particles are annihilated and two photons of equal energy are produced.

Determine the momentum of one of the photons.

[3]

Markscheme

γ = 1.96

E_k = (γ − 1) m₀c² = 900 «Me $\,$ V»

pd ≈ 900 «MV»

Award [2 max] if Energy and Potential difference are not clearly distinguished, eg by the unit.

[3 marks]

energy of proton = γmc² = 1838 «Me $\,$ V»

total energy available = energy of proton + energy of antiproton = 1838 + 1838 = 3676 «Me $\,$ V»

momentum of a one photon = Total energy / 2c = 1838 «Me $\,$ Vc^–1»

[3 marks]

Examiners report

[N/A]

Syllabus sections

Option A: Relativity » Option A: Relativity (Additional higher level option topics) » A.4 – Relativistic mechanics (HL only)

Show 27 related questions

18M.3.HL.TZ1.6b:
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18M.3.HL.TZ2.6a:
Calculate the gamma (γ) factor for one of the protons.
18N.3.HL.TZ0.6a:
Show that the momentum of the electron is 1.41 MeV c^–1.
18N.3.HL.TZ0.6b.i: Explain the origin of each equation.
18N.3.HL.TZ0.6b.ii: Calculate, in MeV c–1, p1 and p2.
19M.3.HL.TZ2.8bi: Determine the momentum of the proton.
16N.3.HL.TZ0.8a: Explain, in terms of a conservation law, why two photons need to be created.
17N.3.HL.TZ0.7b:
Determine, using your answer to (a), the initial speed of the ${\Lambda ^0}$ particle.
16N.3.HL.TZ0.8b:
Determine the speed of the incoming electron.
16N.3.HL.TZ0.8c:
Calculate the energy and the momentum for each photon after the collision.
19M.3.HL.TZ2.8bii:
Determine the speed of the proton.
18M.3.HL.TZ2.6b.i:
Determine, in terms of MeV c^–1, the momentum of the pion.
19M.3.HL.TZ1.6a:
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19N.3.HL.TZ0.5a(i):
the total energy.
19N.3.HL.TZ0.5a(ii):
the speed.
17N.3.HL.TZ0.7a:
Determine the rest mass of the ${\Lambda ^0}$ particle.
19N.3.HL.TZ0.5b:
Determine the rest mass of X.
20N.3.HL.TZ0.6c: In relativistic reactions the mass of the products may be less than the mass of the...
20N.3.HL.TZ0.6a: Define rest mass.
17M.3.HL.TZ2.6:
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$\Lambda$ ⁰ → p + $\pi$ ^–

where the rest energy of p = 938 MeV and the rest energy of $\pi$ ^– = 140 MeV.

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18M.3.HL.TZ1.6a.ii:
show that the energy of the pion is about 140 MeV.
20N.3.HL.TZ0.6b:
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19M.3.HL.TZ2.8a: Define total energy.
19M.3.HL.TZ2.8biii:
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17M.3.HL.TZ1.5b:
The proton collides with an antiproton moving with the same speed in the opposite direction. As a result both particles are annihilated and two photons of equal energy are produced.

Determine the momentum of one of the photons.
19M.3.HL.TZ1.6b:
Calculate the speed of the pion.

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Option A: Relativity » Option A: Relativity (Additional higher level option topics)

Option A: Relativity

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